Sol-Ch02 - CHAPTER 2 E xercises 1(a 4.1 m along the x axis...

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Exercises 1. (a) 4.1 m along the +x axis ; (b) 3.2 m at 70° to the +x axis 2. (a) 3.5 m at 8.2° below the –x axis ; (b) 5.8 m at 52.5° above the –x axis 3. (a) 3 m at 20° below the = +x axis ; (b) 2 m along the +y axis 4. D = C – A – B = 3.85 m at 10.5° below the –x axis 5. The angle between adjacent vector s is (a) 180° ; (b) 90° ; (c) Many possibilities, e.g. 60 ° if equal angles ; (d) 0. 6. (a) 83 °; (b) 151° 7. 60 m at 25° E of N 8. R x =–4 sin 40 ° – 3 cos 20 ° = –5.39 m, R y = 4 cos 40° – 3 sin 20 ° = 2.04 m, R = 5.76 m at 20.7° N of W. 9. R x = A cos 45° + B sin 60 ° – C sin 30° = 3.54 + 6.06 – 2 = 7.60 m, R y = A sin 45° – B cos 60° – C cos 30° = 3.54 – 3.50 – 3.46 = –3.42 m, R = 8.33 at 24.2° S of E. 10. R = –12.1i – 5 j m, or R = 13 m at 22.6° S of W 11. (50 2 – 25 2 ) 1/2 = 43.3 cm 12. y = 100 / ran 30 ° = 173 km 13. (a) A = –i – 1.73 j m, B = 1.53i + 1.29 j m, C = –1.73i + j m, D = 1.64i – 1.15 j m; (b) R = A + B + C + D = 0.44i – 0.59 j m ; CHAPTER 2
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(c) R = 0.74 m at 53.3° below the +x axis. 14. (a) A = –3.63i – 1.69 j m, B = 2.57i – 3.06 j   m, C = –1.37i + 3.76 j   m, D = –4 j   m; (b) R = –2.43i – 4.99 j m ; (c) R = 5.55 m, at 64.0° below the –x axis 15. (a) R = i j m ; (b) R = (2) 1/2 = 1.41 m; (c) R /R = 1/(2) 1/2 (i j ) m = 0.707i – 0.707 j   m 16. (a) S = 2i + 4 j   – 8k m; (b) S = (84) 1/2 m = 9.17 m; (c) S /S = 0.218i + 0.436 j   – 0.873k 17. (a) 0, (b) 180°, (c) (6 + 4 cos θ ) 2 + (4 sin θ ) 2 = 9, so cos θ = –0.896 , And θ = 153°; (d) (6 + 4 cos θ ) 2 + (4 sin θ ) 2 = 64, so cos θ = 0.25 , and θ = 75.5°. 18. Know R = A + B = –6.02i + 7.99 j m, and B = 3.61i + 4.79 j , so A = R – B = –0.63i + 3.2 j , or A = 10.1 m at 18.4° N of W. 19. (a) A = A cos 45°i + A sin 45° j = 1.41i + 1.41 j km, B = B sin75°i + B cos 75° j   = 1.45i + 0.39 j km, and C = –C sin 15°i – C cos 15° j   = 0.39i – 1.45 j   km. Since A + B + C + D = 0, we find D = –2.47i – 0.35 j   km; (b) D = 2.49 km at 8.07° S of W 20. S = A – B = S cos 30°i + S sin 30° j , where S = A / 2 = 3 m. So, B = A – S = 3.40i – 1.5 j m, or B = 3.72 m at 23.8° S of E. 21. The initial and final positions are
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Sol-Ch02 - CHAPTER 2 E xercises 1(a 4.1 m along the x axis...

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